




from __future__ import annotations

import math






def    snake_case(							__magic_name__					,						__magic_name__       )					->				list:





     '''simple docstring'''


     if len(_A       ) != 2 or len(a[0]       ) != 2 or len(_A       ) != 2 or len(b[0]       ) != 2:
          raise Exception('''Matrices are not 2x2'''       )
     lowercase   :  Union[str, Any]        =					[
         [a[0][0] * b[0][0] + a[0][1] * b[1][0], a[0][0] * b[0][1] + a[0][1] * b[1][1]],
         [a[1][0] * b[0][0] + a[1][1] * b[1][0], a[1][0] * b[0][1] + a[1][1] * b[1][1]],
     ]
     return new_matrix






def    snake_case(							__magic_name__					,						__magic_name__       )					->				str:





     '''simple docstring'''


     return [
         [matrix_a[row][col] + matrix_b[row][col] for col in range(len(matrix_a[row]       )       )]
         for row in range(len(_A       )       )
     ]






def    snake_case(							__magic_name__					,						__magic_name__       )					->				List[str]:





     '''simple docstring'''


     return [
         [matrix_a[row][col] - matrix_b[row][col] for col in range(len(matrix_a[row]       )       )]
         for row in range(len(_A       )       )
     ]






def    snake_case(							__magic_name__       )					->				tuple[list, list, list, list]:





     '''simple docstring'''


     if len(_A       ) % 2 != 0 or len(a[0]       ) % 2 != 0:
          raise Exception('''Odd matrices are not supported!'''       )

     lowercase   :  Union[str, Any]        =					len(_A       )
     lowercase   :  List[Any]        =					matrix_length // 2

     lowercase   :  str        =					[[a[i][j] for j in range(_A					,						_A       )] for i in range(_A       )]
     lowercase   :  Dict        =					[
         [a[i][j] for j in range(_A					,						_A       )] for i in range(_A					,						_A       )
     ]

     lowercase   :  Optional[int]        =					[[a[i][j] for j in range(_A       )] for i in range(_A       )]
     lowercase   :  List[str]        =					[[a[i][j] for j in range(_A       )] for i in range(_A					,						_A       )]

     return top_left, top_right, bot_left, bot_right






def    snake_case(							__magic_name__       )					->				tuple[int, int]:





     '''simple docstring'''


     return len(_A       ), len(matrix[0]       )






def    snake_case(							__magic_name__       )					->				None:





     '''simple docstring'''


     print('''\n'''.join(str(_A       ) for line in matrix       )       )






def    snake_case(							__magic_name__					,						__magic_name__       )					->				list:





     '''simple docstring'''


     if matrix_dimensions(_A       ) == (2, 2):
          return default_matrix_multiplication(_A					,						_A       )

     lowercase     ,			lowercase     ,			lowercase     ,			lowercase   :  int        =					split_matrix(_A       )
     lowercase     ,			lowercase     ,			lowercase     ,			lowercase   :  Dict        =					split_matrix(_A       )

     lowercase   :  int        =					actual_strassen(_A					,						matrix_subtraction(_A					,						_A       )       )
     lowercase   :  int        =					actual_strassen(matrix_addition(_A					,						_A       )					,						_A       )
     lowercase   :  int        =					actual_strassen(matrix_addition(_A					,						_A       )					,						_A       )
     lowercase   :  Optional[int]        =					actual_strassen(_A					,						matrix_subtraction(_A					,						_A       )       )
     lowercase   :  Dict        =					actual_strassen(matrix_addition(_A					,						_A       )					,						matrix_addition(_A					,						_A       )       )
     lowercase   :  Union[str, Any]        =					actual_strassen(matrix_subtraction(_A					,						_A       )					,						matrix_addition(_A					,						_A       )       )
     lowercase   :  Tuple        =					actual_strassen(matrix_subtraction(_A					,						_A       )					,						matrix_addition(_A					,						_A       )       )

     lowercase   :  Dict        =					matrix_addition(matrix_subtraction(matrix_addition(_A					,						_A       )					,						_A       )					,						_A       )
     lowercase   :  Union[str, Any]        =					matrix_addition(_A					,						_A       )
     lowercase   :  Optional[int]        =					matrix_addition(_A					,						_A       )
     lowercase   :  int        =					matrix_subtraction(matrix_subtraction(matrix_addition(_A					,						_A       )					,						_A       )					,						_A       )

     # construct the new matrix from our 4 quadrants
     lowercase   :  Dict        =					[]
     for i in range(len(_A       )       ):
          new_matrix.append(top_left[i] + top_right[i]       )
     for i in range(len(_A       )       ):
          new_matrix.append(bot_left[i] + bot_right[i]       )
     return new_matrix






def    snake_case(							__magic_name__					,						__magic_name__       )					->				list:





     '''simple docstring'''


     if matrix_dimensions(_A       )[1] != matrix_dimensions(_A       )[0]:
          lowercase   :  str        =					(
              '''Unable to multiply these matrices, please check the dimensions.\n'''
              F"""Matrix A: {matrixa}\n"""
              F"""Matrix B: {matrixa}"""
          )
          raise Exception(_A       )
     lowercase   :  Any        =					matrix_dimensions(_A       )
     lowercase   :  Dict        =					matrix_dimensions(_A       )

     if dimensiona[0] == dimensiona[1] and dimensiona[0] == dimensiona[1]:
          return [matrixa, matrixa]

     lowercase   :  str        =					max(*_A					,						*_A       )
     lowercase   :  Dict        =					int(math.pow(2					,						math.ceil(math.loga(_A       )       )       )       )
     lowercase   :  Dict        =					matrixa
     lowercase   :  Any        =					matrixa

     # Adding zeros to the matrices so that the arrays dimensions are the same and also
     # power of 2
     for i in range(0					,						_A       ):
          if i < dimensiona[0]:
               for _ in range(dimensiona[1]					,						_A       ):
                    new_matrixa[i].append(0       )
          else:
               new_matrixa.append([0] * maxim       )
          if i < dimensiona[0]:
               for _ in range(dimensiona[1]					,						_A       ):
                    new_matrixa[i].append(0       )
          else:
               new_matrixa.append([0] * maxim       )

     lowercase   :  Union[str, Any]        =					actual_strassen(_A					,						_A       )

     # Removing the additional zeros
     for i in range(0					,						_A       ):
          if i < dimensiona[0]:
               for _ in range(dimensiona[1]					,						_A       ):
                    final_matrix[i].pop()
          else:
               final_matrix.pop()
     return final_matrix


if __name__ == "__main__":
 lowerCAmelCase_						 =					[
     [2, 3, 4, 5],
     [6, 4, 3, 1],
     [2, 3, 6, 7],
     [3, 1, 2, 4],
     [2, 3, 4, 5],
     [6, 4, 3, 1],
     [2, 3, 6, 7],
     [3, 1, 2, 4],
     [2, 3, 4, 5],
     [6, 2, 3, 1],
 ]
 lowerCAmelCase_						 =					[[0, 2, 1, 1], [16, 2, 3, 3], [2, 2, 7, 7], [13, 11, 22, 4]]
 print(strassen(matrixa, matrixa))



def 							UpperCamelCase_(					_A :Union[str, Any]	)->		List[str]:
			UpperCamelCase__       =							[0] * len(_A	)
			UpperCamelCase__       =							[]
			UpperCamelCase__       =							[]
			UpperCamelCase__       =							0

			for values in graph.values():
						for i in values:
									indegree[i] += 1

			for i in range(len(_A	)	):
						if indegree[i] == 0:
									queue.append(_A	)

			while queue:
						UpperCamelCase__       =							queue.pop(0	)
						cnt += 1
						topo.append(_A	)
						for x in graph[vertex]:
									indegree[x] -= 1
									if indegree[x] == 0:
												queue.append(_A	)

			if cnt != len(_A	):
						print("Cycle exists"	)
			else:
						print(_A	)


# Adjacency List of Graph
__UpperCamelCase     		=							{0: [1, 2], 1: [3], 2: [3], 3: [4, 5], 4: [], 5: []}







topological_sort(graph)


